{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "sarsa.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyM2WMxoThIS2veShVBHNn0O",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/letianzj/QuantResearch/blob/master/ml/sarsa.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JlNkxcEuDTVn",
        "colab_type": "text"
      },
      "source": [
        "## SARSA FrozenLake\n",
        "\n",
        "Use SARSA to solve FrozenLake game.\n",
        "\n",
        "[OpenAI Gym FrozenLake](https://gym.openai.com/envs/FrozenLake-v0/) is defined on a 4x4 matrix. The agent wants to go from top left (S) to bottom right (G). Each grid can be either frozen surface (F) or hold (H). Four possible actions or moves are Left: 0, Down: 1, Right: 2, Up: 3. If the agent reaches goal (G), she receives reward of 1.\n",
        "\n",
        "SARSA is on policy, value based, TD method to solve control problems. The Q-value is updated by\n",
        "\n",
        "$$\n",
        "Q(s, a) \\leftarrow Q(s,a) + \\alpha \\left( r+\\gamma Q(s',a') - Q(s,a) \\right)\n",
        "$$\n",
        "\n",
        "__Reference__\n",
        "* Sutton, Richard S., and Andrew G. Barto. Reinforcement learning: An introduction. MIT press, 2018.\n",
        "* [RL by David Silver](https://www.davidsilver.uk/teaching/)\n",
        "* [Lil'Log](https://lilianweng.github.io/lil-log/)\n",
        "* [Deep Learning with TensorFlow](https://github.com/dragen1860/Deep-Learning-with-TensorFlow-book)\n",
        "* [Reinforcement Learning](https://github.com/dennybritz/reinforcement-learning)\n",
        "* [marcinbogdanski](https://marcinbogdanski.github.io/reinforcement-learning.html)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0lOf7OSWHOvv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import gym"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xtBE-yWBHZZh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "env = gym.make('FrozenLake-v0', is_slippery=True)   # may not head for the direction chosen"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0QH8az9cJpmI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "n_episodes = 1000\n",
        "alpha = 0.5                 # TD learning rate\n",
        "epsilon = 0.1               # epsilon greedy\n",
        "epsilon_final = 0.05\n",
        "epsilon_decay = (epsilon-epsilon_final)/n_episodes   # epsilon annealing\n",
        "gamma = 0.99                # discount factor\n",
        "\n",
        "# Q-Table, default to 0\n",
        "Q = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "# action space\n",
        "actions = range(env.action_space.n)"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vQotgJIHK4EW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "3023fd1a-00cf-4bde-9d18-7d788cb13e3b"
      },
      "source": [
        "reward_history = []\n",
        "step_history = []\n",
        "\n",
        "for n_episode in range(n_episodes):\n",
        "    s = env.reset()          # reset to initial state\n",
        "    # env.render()\n",
        "    done = False\n",
        "    reward = 0.\n",
        "    step = 0\n",
        "\n",
        "    # choose action according to epsilon greedy\n",
        "    a = 0\n",
        "    if np.random.rand() < epsilon:\n",
        "        a = env.action_space.sample()\n",
        "    else:   # randomly pick one in case of a tie\n",
        "        candidates = np.argwhere(Q[s, :] == np.amax(Q[s, :]))\n",
        "        candidates = candidates.reshape(-1,)\n",
        "        a = np.random.choice(candidates)\n",
        "\n",
        "    while not done:\n",
        "        # use a' to interact with environment\n",
        "        s_prime, r, done, info = env.step(a)\n",
        "        step += 1\n",
        "        reward += r\n",
        "\n",
        "        # choose action_prime according to epsilon greedy\n",
        "        a_prime = 0\n",
        "        if np.random.rand() < epsilon:\n",
        "            a_prime = env.action_space.sample()\n",
        "        else:   # randomly pick one in case of a tie\n",
        "            candidates = np.argwhere(Q[s_prime, :] == np.amax(Q[s_prime, :]))\n",
        "            candidates = candidates.reshape(-1,)\n",
        "            a_prime = np.random.choice(candidates)\n",
        "        \n",
        "        # update q table\n",
        "        Q[s, a] = Q[s, a] + alpha * (r + gamma * Q[s_prime, a_prime] - Q[s, a])\n",
        "\n",
        "        # ready for next step\n",
        "        s = s_prime\n",
        "        a = a_prime\n",
        "\n",
        "    reward_history.append(reward)\n",
        "    step_history.append(step)\n",
        "\n",
        "    epsilon -= epsilon_decay\n",
        "\n",
        "    if (n_episode + 1) % 200 == 0:\n",
        "        print(f'Episode {n_episode + 1}/{n_episodes}.')"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Episode 200/1000.\n",
            "Episode 400/1000.\n",
            "Episode 600/1000.\n",
            "Episode 800/1000.\n",
            "Episode 1000/1000.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oJ5zWez2_dle",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "env.close()"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iFX-ogw0zSQk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 353
        },
        "outputId": "e27a7e58-7247-4da7-edef-3c3e47f0a15b"
      },
      "source": [
        "df_stats = pd.DataFrame.from_dict({'rewards': reward_history, 'steps': step_history})\n",
        "fig, ax = plt.subplots(1, 2, figsize=(16,5))\n",
        "df_stats['rewards'].rolling(100).mean().plot(ax=ax[0])\n",
        "ax[0].set_title('Average rewards')\n",
        "df_stats['steps'].rolling(100).mean().plot(ax=ax[1])\n",
        "ax[1].set_title('Average steps')"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Average steps')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lAmz6UWC_mex",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}